In radioactive measuring methods involving the use of X-rays or gamma rays for example, for measuring densities, content levels or flow rates, or for monitoring limiting levels the effects of extraneous radiation cause faulty measurements. The term "extraneous radiation" does not refer to background radiation in the form of cosmic or terrestrial radiation, but rather the effects of intermittently active radiation sources which are used, for example, in the course of non-destructive testing of materials (gamma-graphics, back-scattering examinations) as well as X-ray diagnostics, etc. The occurrence of such extraneous radiation may be detected by auxiliary radiation detectors which are not exposed to the measuring radiation or by the corruptions of the measurement result caused by it. It is known to detect and indicate the commencement and termination of an extraneous radiation in order to alert the user of the measuring method that the measured value is being distorted by extraneous radiation. It is not feasible, however, to obtain a valid measuring result from the radioactive measurement while the extraneous radiation subsists.